This thesis provides a report on the numerical analysis of stress distributions within granular materials held in silos and hoppers. Stress distributions within granular materials stored in silos and hoppers have been the subject of research for over 100 years, work starting in this field in 1895 (Janssen). Knowledge of stress distributions within the granular materials contained is essential to allow structural design of the silo and hopper shell and attachments, and to allow estimation of likelihood and location of cohesive arch formation. National design codes for silos and hoppers (including BS EN 1993-4-1:2007 Eurocode 3 and DIN 1055-6:2005-03) are based on approximate techniques that assume vertical and horizontal directions of principal stresses, with constant horizontal stress across the silos. According to the knowledge of the author there are no industrial standards that allow calculation of loading on inserts within hoppers. The objective of the research project is to develop algorithms to predict stresses in hoppers and silos using principal stress arc geometry methods, and implementation of these methods in various silo and hopper configurations including those with inserts for the purposes of aiding flow. The research project algorithms are spreadsheet- and QB64 platform-based, and are able to produce stress distributions within silos and hoppers. This is achieved by extension of the principal stress arc method of analysis. The new algorithms allow prediction of common flow problems and provide new information on structural loading of silos and hoppers, including inserts used to promote flow. The research project models allow estimation of azimuthal stresses within three-dimensional case studies.